# Phase difference between electric and magnetic dipole moment

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• kelly0303
kelly0303
Hello! This question is in relation to parity violation (PV) measurements using the optical rotation technique (I can give more details/references about that, but most of it is not relevant for my question). Basically, in a simplified model, they have 2 levels (say of positive parity), g and ##e_1## connected by a magnetic dipole amplitude ##A_{M_1} = <g|M_1|e_1>##. Another level ##e_2## close to ##e_1## (such that we can ignore its effect on g) has negative parity, thus, due to parity violation Hamiltonian, ##H_{PV}##, ##e_1## becomes:

$$|e_1'>=|e_1>+\frac{<e_1|H_{PV}|e_2>}{E_2-E_1}|e_2> = |e_1>+i\eta|e_2>$$
where ##E_1## and ##E_2## are the energies of the ##e_1## and ##e_2## levels (I might have messed up some signs, but that shouldn't matter for my question) and it can be shown that in general, the PV matrix element is always a purely imaginary number, hence ##i\eta = \frac{<e_1|H_{PV}|e_2>}{E_2-E_1}##. Now, in the experiments, people make use of the interference between the M1 transition and the PV effect, in order to amplify the latter one. In the 2D space spanned by g and ##e_1'##, the off diagonal matrix element is:

$$<g|M_1|e_1>+i\eta<g|E_1|e_2> = A_{M_1} + i\eta A_{E_1}$$
and the rate is the square of its modulus. However, in order to get interference i.e. a term proportional to ##\eta A_{M_1}A_{E_1}##, both terms must be either real or imaginary. However, given that ##i\eta## is purely imaginary, this implies, that in order to get the interference ##A_{M_1}## and ##A_{E_1}## should be one purely real and the other one purely imaginary. However, I am not sure I understand why and which is which. Can someone help me figure this out? Thank you!

## What is the phase difference between electric and magnetic dipole moments?

The phase difference between electric and magnetic dipole moments refers to the angular difference in the oscillation cycles of the electric and magnetic fields in an electromagnetic wave. Typically, in a plane electromagnetic wave propagating in free space, the electric and magnetic fields are in phase, meaning their oscillations reach their maximum and minimum values simultaneously.

## How does the phase difference between electric and magnetic dipole moments affect electromagnetic wave propagation?

The phase difference between the electric and magnetic dipole moments is crucial for the coherent propagation of electromagnetic waves. If the electric and magnetic fields are not in phase, the wave may not propagate effectively, leading to energy dissipation or wave distortion. In free space, these fields are generally in phase to ensure efficient energy transfer.

## Can the phase difference between electric and magnetic dipole moments be manipulated or controlled?

Yes, the phase difference between electric and magnetic dipole moments can be manipulated using various materials and structures, such as metamaterials and waveguides. These materials can alter the propagation characteristics of electromagnetic waves, including their phase relationship, to achieve desired effects like negative refraction or cloaking.

## What role does the phase difference play in antenna design?

In antenna design, maintaining the correct phase relationship between the electric and magnetic dipole moments is essential for efficient radiation and reception of electromagnetic waves. Antennas are designed to ensure that the electric and magnetic fields are in phase at the point of radiation, maximizing the antenna's performance and signal strength.

## How is the phase difference between electric and magnetic dipole moments measured?

The phase difference between electric and magnetic dipole moments can be measured using specialized equipment such as vector network analyzers and oscilloscopes. These instruments can analyze the phase and amplitude of the electric and magnetic fields, allowing scientists to determine the phase relationship and make necessary adjustments for optimal performance.

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